AS CONTAS DA LOUCURA

Texto e gráfico original aqui onde podem ser visualizadas as projecções para Portugal

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The maths behind the madness

Our interactive guide to government-debt dynamics
 

 

ALL EYES are on Spain ahead of the European Council's two-day meeting in Brussels beginning on October 18^th. In just three short years, the country's horrendous housing bust and subsequent recession have caused government debt to increase from a sustainable 40% of GDP in 2008 to 70% of GDP in 2011. Despite brutal government spending cuts, by the end of this year the IMF forecasts government debt will reach 90% of GDP. The question of whether Spain will seek a bail-out preoccupies markets and policymakers alike.

Our interactive graphic above shows the IMF's latest forecasts (updated in October 2012) for government gross debt as a percentage of GDP through to 2017. It also allows you to input your own long-term assumptions to project the likely path of debt to 2020.

There are two things that matter in government-debt dynamics: the difference between real interest rates and GDP growth (r-g), and the primary budget balance as a % of GDP (ie, before interest payments). In any given period the debt stock grows by the existing debt stock (d) multiplied by r-g, less the primary budget balance (p).

The simple r-g assumption is one of the most important in debt dynamics: an r-g of greater than zero (when interest rates are greater than GDP growth) means that the debt stock increases over time. An r-g of less than zero causes it to fall.

Our interactive model uses the nominal interest rate (i) approximately equivalent to the ten-year bond yield and allows you to input your own inflation rate, π. Inflation helps reduce the total debt stock over time, by reducing the real value of debt. In our model and using approximations, r-g becomes i - π - g. The greater the inflation rate, the lower r-g becomes.

The second consideration is the primary budget balance. A primary budget surplus causes the debt stock to fall, by allowing the government to pay off some of the existing debt. A primary deficit needs to be financed by further borrowing. As European peripheral countries have found out to their cost, interest rates increase when governments run large budget deficits, and as they do it becomes increasingly difficult to reduce r-g to a sustainable level.

In reality, these variables are all related. When inflation rises, for instance, bondholders will expect a higher nominal interest rate on new debt. If a country runs a larger primary surplus, the interest rate it is forced to pay may fall. Adjustments in countries' deficits will also affect their growth rates. To keep matters simple, we have ignored these interactions. Our calculator shows the evolution of a government's debt stock based directly on the values for inflation, growth, interest rates and the primary deficit that you determine.

Spain has lots of work to do. Keeping all things equal, the country would need to grow by 7.7% a year, or nominal bond yields to fall to a Teutonic 0.5% to stabilise government gross debt at its 2011 level of 70% of GDP. Fat chance: the IMF forecasts GDP growth to average just 0.5% a year and bond yields of 7.7% between 2012 and 2017. A bail-out for Spain it seems, is not a case of if, but when.